Harmonic Analysis of Operators on Hilbert SpaceSpringer Science & Business Media, 1 בספט׳ 2010 - 478 עמודים The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition. |
תוכן
Chapter I | 1 |
Chapter II | 59 |
Chapter III | 103 |
Chapter IV | 159 |
Chapter V | 188 |
Chapter VI | 243 |
Chapter VII | 288 |
Chapter VIII | 331 |
Chapter IX | 361 |
Chapter X | 397 |
Bibliography | 441 |
Notation Index | 465 |
Author Index | 467 |
| 471 | |
מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
Acta Sci apply arbitrary Assume belongs bounded called characteristic function choose closed coincides commuting completely conclude condition consequently consider constant construct contained continuous contractive analytic function converges Corollary corresponding cyclic decomposition deduce defect defined definition denote dense determined divisor element equal example exists extended fact factorization finite follows functional calculus given hand hence Hilbert space holds implies indices inequality inner function integral invariant subspace invertible isometric Lemma limit linear Math matrix maximal measure Moreover nonzero observe obtain obviously orthogonal outer particular positive problem projection Proof properties Proposition proved purely reduces regular relation Remark representation respectively result satisfying scalar multiple semigroup sequence similar spectral spectrum Szeged Theorem theory tion transformation unilateral shift unique unit unitarily equivalent unitary operator values vectors virtue zero